Why are the solutions to the proportions 40/8 = x/10 and x/40 = 10/8 the same?
2 answers:
Answer:
Both proportions are equivalent.
Step-by-step explanation:
We have been given two proportions and
. We are asked to find why the solutions to our given proportions are equal.
We can solve proportions by cross multiplying them.
After cross multiplying our both proportions we will get same equation that is:
Since we get same equation after cross multiplying both proportions, therefore, the solutions to the given proportions would be same.
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Answer:
a) 0.1587 (or 15.87%)
b) 0.0478 (or 4.78%)
c) 0.7935 (or 79.35%)
Step-by-step explanation:
Find the following probabilities:
(a) the thickness is less than 3.0 mm
We need to find the area under the Normal curve with a mean of 4.5 mm and a standard deviation of 1.5 mm to the left of 3 mm
<h3>(See picture 1 attached) </h3>We can do that with the help of a calculator or a spreadsheet.
<em>In Excel use </em>
<em>NORMDIST(3,4.5,1.5,1) </em>
<em>In OpenOffice Calc use </em>
<em>NORMDIST(3;4.5;1.5;1) </em>
and we get the value 0.1587 (or 15.87%)
(b) the thickness is more than 7.0 mm
Now we need the area to the right of 7 (1 - the area to the left of 7)
<h3>(See picture 2 attached) </h3><em>In Excel use </em>
<em>1-NORMDIST(7,4.5,1.5,1) </em>
<em>In OpenOffice Calc use </em>
<em>1-NORMDIST(7;4.5;1.5;1) </em>
and we get the value 0.0478 (or 4.78%)
(c) the thickness is between 3.0 mm and 7.0 mm
We are looking for the area between 3 and 7
<h3>(See Picture 3) </h3>Since the area under the Normal equals 1, we have
Area to the left of 3 + Area between 3 and 7 + Area to the right of 7 = 1
Hence,
0.1587 + Area between 3 and 7 + 0.0478 = 1
and
Area between 3 and 7 = 1 - 0.1587 - 0.0478 = 0.7935 (or 79.35%)
